From 4cb51342ab5328b7e3520d5c73782c30d3aed379 Mon Sep 17 00:00:00 2001 From: Nils Forssen Date: Thu, 18 Feb 2021 22:39:55 +0100 Subject: [PATCH] to work on laptop --- .gitignore | 23 + Archimedes.py | 25 + Buffon'sNeedle.py | 23 + Buffon'sNeedle.xlsx | Bin 0 -> 4225226 bytes CalcVariance.py | 43 + needle.txt | 10000 ++++++++++++++++++++++++++++++++++++++++++ 6 files changed, 10114 insertions(+) create mode 100644 Archimedes.py create mode 100644 Buffon'sNeedle.py create mode 100644 Buffon'sNeedle.xlsx create mode 100644 CalcVariance.py create mode 100644 needle.txt diff --git a/.gitignore b/.gitignore index f717486..7838b39 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,22 @@ +# Package init +__init__.py + +#test.py +test.py + +# Cache files for Sublime Text +*.tmlanguage.cache +*.tmPreferences.cache +*.stTheme.cache + +# Workspace files are user-specific +*.sublime-workspace +*.sublime-project + +# Project files should be checked into the repository, unless a significant +# proportion of contributors will probably not be using Sublime Text +# *.sublime-project + # Byte-compiled / optimized / DLL files __pycache__/ *.py[cod] @@ -123,3 +142,7 @@ dmypy.json # Pyre type checker .pyre/ +Buffon'sNeedle3.txt +Buffon'sNeedle2.txt +Buffon'sNeedle1.txt +Buffon'sNeedle.txt diff --git a/Archimedes.py b/Archimedes.py new file mode 100644 index 0000000..bed7d9f --- /dev/null +++ b/Archimedes.py @@ -0,0 +1,25 @@ +from Equation import Expression +import random +import math + + +fn1 = Expression("sqrt(2 - 2 * sqrt(1 - (l/2)^2))", ["l", "r"]) +fn2 = Expression("sqrt(q^2/(2+2 * sqrt(1 - (q/2)^2)))", ["q", "p"]) +fn31 = Expression("(2+2 * sqrt(1 - (y/2)^2))", ["y", "t"]) +fn32 = Expression("sqrt(o^2/e)", ["o", "e"]) +r = 1 +l1 = 1 +l2 = 1 +l3 = 1 +middle = None +n = 6 + +while True: + print(f"1 : n = {n} pi = {n * l1 / 2} l = {l1} t = {1 - (l1/2)**2}") + print(f"2 : n = {n} pi = {n * l2 / 2} l = {l2} t = {1 - (l1/2)**2}") + print(f"3 {l3 == l2} middle = {middle}") + n *= 2 + l1 = fn1(l1, r) + l2 = fn2(l2, r) + middle = fn31(l3, r) + l3 = fn32(l3, middle) diff --git a/Buffon'sNeedle.py b/Buffon'sNeedle.py new file mode 100644 index 0000000..cd84b77 --- /dev/null +++ b/Buffon'sNeedle.py @@ -0,0 +1,23 @@ +from Equation import Expression +import random +import math +fn = Expression("length*sin(theta)/2", ["length", "theta"]) +l = 1 +d = 2 +n = 0 +N = 0 +with open("needle.txt", "w") as file: + while True: + N += 1 + x = random.uniform(0, math.pi / 2) + y = random.uniform(0, d / 2) + + # Evaluate if point is within subset + n += (fn(length=l, theta=x) >= y) + + # Print the estimate for every value of N + if not N % 100: + file.write(f"{N}\t{(2*l)/((n/N)*d)}\n") + + if N == 1e6: + break diff --git a/Buffon'sNeedle.xlsx b/Buffon'sNeedle.xlsx new file mode 100644 index 0000000000000000000000000000000000000000..ea0929a1e9a802ec89c1778a22de0c18739a95fb GIT binary patch literal 4225226 zcmeFXuJW8^lU}!)PKu|zHK*T_%q$_4fAV5Hkus}elKu{pMqK*!3<_>O#YTi!fuKEmK 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